Section 3.3.7.1. Growth twinning

(a) An alternative theory of twinning postulates the formation of a two-dimensional nucleus in twin position on a growth face of an existing macroscopic (previously untwinned) crystal. Such a mechanism was extensively described by Buerger (1945, pp. 472–475) and followed up by Menzer (1955) and Holser (1960). Obviously, this process is favoured by defects (inclusions, impurities) in the growth face. If the twin nucleus spreads out over the entire growth face, the twin boundary coincides with the growth face. This mechanism is generally assumed for the generation of large-area lamellar polysynthetic growth twins as observed for albite (Example 3.3.6.11 and Fig. 3.3.6.11). For a critical discussion of the origin of irrational twin interfaces in rotation twins such as the pericline twins see Cahn (1954, p. 408). It should be noted that this mechanism is possible only for twin boundaries of very low energy, since the boundary energy of the large interface has to be supplied in one step, i.e. during spreading out of one growth layer in twin position. It is obvious that this kind of twin formation can only occur if the twin boundary coincides with a prominent growth face (F-face, rarely S-face, according to Hartman, 1956).

(b) In the majority of growth twins, the twin boundary does not coincide with the growth face. This is the rule for merohedral twins, where the twin domains appear as `inserts' in the shape of pyramids or lamellae extending from the initiating defects (mostly inclusions) into the direction of growth of the face on which the twin has started. Examples are the pyramid-shaped Brazil-twin inserts of quartz (Frondel, 1962, Fig. 61 on p. 87) and the lamellar stripes of growth twins of KLiSO₄ (Klapper et al., 1987, especially. Fig. 5). Similar pyramidal twin inserts are observed for Dauphiné growth twins in natural and synthetic quartz. These twin morphologies in quartz, however, are often considerably modified after growth by (partial) ferrobielastic switching of the domains, which is easily induced by stress at elevated temperatures [cf. Section 3.3.7.3(iii)]. Illustrations of such Dauphiné twins are given by Frondel (1962, Fig. 49 on p. 78).

The growth-twin inserts as described above appear improbable for non-merohedral twins because unfavourable high-energy boundaries would be involved. As a consequence, it must be concluded that non-merohedral twins with boundaries not coinciding with a (prominent) growth face (e.g. dovetail twins of gypsum) must form during the nucleation stage of the crystal [Section 3.3.7.1.1 above].

(c) Another model of twin formation has been suggested by Schaskolsky & Schubnikow (1933). It is based on the idea that in the melt or solution the pre-existing small crystals make accidental contact with analogous faces and parallel, rotate and agglutinate in twin position, and continue to grow as a twin. This concept is also favoured by Buerger (1960b). The model of Schaskolsky & Schubnikow is based on their interesting experiments with many () K-alum crystals (up to 0.5 mm in size), which sediment in solution on horizontal octahedron (111) and cube (100) faces of large alum crystals (20–30 mm in size). A statistical analysis of the orientation distribution of the sedimented crystals reveals a significantly increased frequency of (111)/(111) parallel intergrowths, of regular (001)/(111) intergrowths and of (111) spinel twins. The authors interpret this result as a rotation of the small crystals around the contact-face normal after deposition on the large crystal. This initial contact plane (ICP) model of twin formation was critically discussed by Senechal (1980) and considered as questionable, an opinion which is shared by the present authors.

(d) Finally, it is pointed out that twinning may drastically modify the regular growth morphology of (untwinned) crystals. A prominent example is the tabular shape of (111)-twinned cubic crystals with the large face parallel to the (111) contact plane. This is due to the increased lateral growth rate of the faces meeting in re-entrant edges (re-entrant corner effect; Hartman, 1956; Ming & Sunagawa, 1988). The (111) tabular shape of twinned cubic crystals plays an important role for photographic materials such as silver bromide, AgBr (Buerger, 1960b; Bögels et al., 1997, 1998). A more extreme habit modification is exhibited by the growth needles of cubic AgBr, which contain two twin planes intersecting along (Bögels et al., 1999).

The phenomenon of habit modification by twinning has been developed further by Senechal (1976, 1980), who presents an alternative model of the genesis of penetration twins (cf. Section 3.3.7.1.1 above): initial cubic (111) contact twins consisting of two octahedra change their habit during growth so as to form two interpenetrating cubes of the spinel law. As a further example, chabasite is cited.

(e) During melt growth of the important cubic semiconductors with the diamond structure (Si, Ge) and sphalerite (zinc sulfide) structure (e.g. indium phosphide, InP), twins of the spinel law [twin mirror plane (111) or twofold twin axis [111], cf. Section 3.3.10.3.3] are frequently formed. Whereas this twinning is relatively rare and can easily be avoided for Si and Ge, it is a persistent problem for the III–V and II–VI compound semiconductors, especially for InP and CdTe crystals, which have a particularly low {111} stacking-fault energy (Gottschalk et al., 1978). For Czochralsky growth, these twins are usually nucleated at `edge facets' forming at the surface of the `shoulder' (or `cone region') where the growing crystal widens from the seed rod to its final diameter. Once nucleated, they proceed during further growth as bulk twins or, more frequently, as twin lamellae with sharp contact planes. For a [111] pulling direction, the three equivalent {111} twin planes with inclination of 19.5° against the pull axis [111] are usually activated, whereas the perpendicular (111) twin plane does not or only rarely occurs (Bonner, 1981; Tohno & Katsui, 1986). These twins can be avoided by optimizing the growth conditions, in particular by the choice of a proper cone angle, which is the most crucial parameter. A mechanism of the {111} twin formation of III–V compound semiconductors was suggested by Hurle (1995) and experimentally confirmed for InP, using synchroton-radiation topography combined with chemical etching and Normarski microscopy, by Chung et al. (1998) and Dudley et al. (1998). A comprehensive X-ray topographic study of (111) twinning in indium phosphide crystals, grown by the liquid-encapsulated Czochralski technique, and its interaction with dislocations is presented by Tohno & Katsui (1986).

(f) It should be noted lastly that `annealing twins' (which are an important subject in metallurgy) are not treated in this section, because they are considered to be part of bicrystallography. These twins are formed during recrystallization and grain growth in annealed polycrystalline materials (cf. Cahn, 1954, pp. 399–401).